How many different ways can a team of 2 men and 2 women be formed if there are 4 men and 5 women from which to select?
You are choosing 2 men from 4, and 2 women from 5, so that simply
becomes:
C(4,2) * C(5,2)
= 6*10
= 60
How many ways can you make a team of 2 men from 4 men ?
n!/ [ r!(n-r)! ] = 4! / [ 2(2) ] = 3*2*1 = 6
How many ways a team of 2 women from 5 women?
5!/[2 (3*2) ] = 5*4 / 2 = 10
6*10 = 60
To find the number of different ways to form a team of 2 men and 2 women from a group of 4 men and 5 women, we can use the combination formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items to be selected.
In this case, we want to select 2 men from a group of 4 men, which can be done in 4C2 = (4!)/(2!(4-2)!) = (4!)/(2!2!) = (4 ✕ 3)/(2 ✕ 1) = 6 ways.
Similarly, we want to select 2 women from a group of 5 women, which can be done in 5C2 = (5!)/(2!(5-2)!) = (5!)/(2!3!) = (5 ✕ 4)/(2 ✕ 1) = 10 ways.
To find the total number of ways to form the team, we multiply the number of ways to select men and women together:
Total ways = 6 ✕ 10 = 60
Therefore, there are 60 different ways to form a team of 2 men and 2 women from a group of 4 men and 5 women.
To solve this problem, we can use the combination formula.
The combination formula is given by C(n, r) = n! / (r!(n - r)!), where n is the total number of objects and r is the number of objects taken at a time.
In this case, we need to select 2 men from a pool of 4 men, which can be done in C(4, 2) ways. Similarly, we need to select 2 women from a pool of 5 women, which can be done in C(5, 2) ways.
To find the total number of different ways the team can be formed, we need to multiply these two combinations since we want both conditions to be satisfied.
So, the total number of different ways the team can be formed is C(4, 2) * C(5, 2).
Calculating the combinations:
C(4, 2) = 4! / (2!(4 - 2)!) = (4 * 3) / (2 * 1) = 6
C(5, 2) = 5! / (2!(5 - 2)!) = (5 * 4) / (2 * 1) = 10
Now, let's multiply these two combinations:
6 * 10 = 60
Therefore, there are 60 different ways a team of 2 men and 2 women can be formed from a pool of 4 men and 5 women.